This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. The difficulty with multiscale models is the coupling between the distinct models: How does one incorporate MD simulations as e.g. boundary conditions for the elasticity equations, and how does one incorporate the large-scale deformation of the solid as boundary information in the MD simulation? There are many ad-hoc techniques proposed to do the coupling (quasi-continuum, heterogeneous multiscale, variational multiscale, and other techniques) but there is very little mathematical theory for anything but extremely simple problems. This is one of the biggest active areas in applied mathematics, with funding agencies such as the U.S. Department of Energy putting substantial resources into this area of applied mathematics in the last fives years due to the relevance to the important complex mathematical models arising in stockpile stewardship programs. Many of the core ideas that were developed for both multilevel fast PDE solvers and adaptive numerical methods for PDE are now resurfacing in this field. We see this as one of several unique opportunities for NBCR to focus these new technologies for the benefit of the biomedical community, with a key role being played by mathematicians at NBCR/UCSD.